Accelerometers in your

Modern cars have airbags which inflate in crashes to protect drivers and passengers from sudden accelerations. Micro-electro-mechanical semiconductor acceleration sensors (accelerometers) are located in bumpers which quickly inflate the airbags. The basic accelerometer is a mass m attached by a spring of constant k to the frame of the sensor device, itself secured to the automobile frame. If the car frame (and thus the frame of the sensor device) undergo a strong acceleration, the spring connecting the mass to the sensor frame will extend or contract, leading to a motion of the mass m relative to the frame of the sensor device. This deflection is measured, for example, by change in a capacitance, which then triggers expansion of the air-bag. This microelectromechanical (MEM) device is mass-produced in an integrated package including relevant electronics, using the methods of silicon microelectronics.

Newton's laws of motion describe the position, x, the velocity, v = dx/dt, and the acceleration a =d2%/di2of a mass m which may be acted upon by a force F> accor-

Kinematics describes the relations among x, v, a, and t. As an example, the time-dependent position x under uniform acceleration a is x~x0 + v0t + at2, (1.3)

where x0 and v0, respectively, are the position and velocity at t« 0. Also, if a time-varying acceleration a(t) is known, and 0 and 0, then x(t)~Ha(t)dt2. (1.4)

Newton's First Law states that in the absence of a force, the mass m remains at rest if initially so, and if initially in motion continues unchanged in that motion. (These laws are valid only if the coordinate system in which the observations are made is one of uniform motion, and certainly do not apply in an accelerated frame of reference such as a carrousel or a merry-go-round. For most purposes the earth's surface, although accelerated toward the earth's rotation axis, can be regarded as an "inertial frame of reference", i.e., Newton's Laws are useful.) The Second Law is F -mat (1.2).

The Third Law states that for two masses in contact, the force exerted by the first on the second is equal and opposite to the force exerted by the second on the

A more sophisticated version of such an accelerometer, arranged to record accelerations in x,y,z directions, and equipped with integrating electronics, can be used to record the three-dimensional displacement over time.

These devices are not presently built on a nanometer scale, of course, but are one example of a wide class of microelectronic sensors that could be made on smaller scales as semiconductor technology advances, and if smaller devices are useful.

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